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Mixed number addition with regrouping

Sal practices adding mixed numbers with common (like) denominators. Items require regrouping.

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Video transcript

- [Narrator] Let's see if we can add five and 2/5 to three and 4/5. Pause this video and see if you can figure out what this is. All right, now let's do this together. We've had a little bit of practice adding mixed numbers in the past. And so one way to think about it is, you could view five and 2/5 as five plus 2/5. And then to that we're going to be adding three and 4/5, which you could view as three plus 4/5. And then you could just change the order with which you are adding, and say, all right, well, I could say five plus three, so that's five plus three, and then to that I could add 2/5 and 4/5, so, plus 2/5, plus 4/5. Now what is that going to get me? Well five plus three is going to be equal to eight. Eight plus, and then if I have 2/5, and I add four more fifths to that, well now I'm going to have 6/5. Two of something plus four of that something is going to be six of that something, and the something in this case are fifths. So now I'm going to have 6/5. So some of you might be tempted to say, "Hey, isn't this just going to be equal to eight and 6/5?" And you wouldn't be completely wrong if you said that. But pause this video and think about why this feels a little bit off. Well, the reason why this isn't standard, is the fractional part of this mixed number 6/5 is greater than one. So there's a whole inside of this 6/5. So the standard way to do this is see if we can break out that whole. Now what do I mean by that? Well I could rewrite eight plus 6/5 as eight plus 6/5 is the same thing as a whole, or 5/5 plus 1/5. And why is this useful? Well 5/5 is the same thing as one. And so now I can say this is going to be equal to eight plus one whole is nine, that's eight plus the 5/5, and then what I have leftover is 1/5. So nine and 1/5. And so this is the direction that people will traditionally go in. Now there's another way that you could approach it, which is really the same idea, we're just writing things a little bit differently. We could write this as five and 2/5 plus three and 4/5, and notice the way that I wrote it. I put all the fractions in the fraction column, I guess you could call it that way, and I put all of our whole numbers underneath each other, and if I had multiple digits here, I would align them according to place value. And then what we could do is we could say, okay 2/5 plus 4/5 is going to be 6/5. We could write 6/5 there. But we say, hey, there's something a little bit fishy about 6/5. That's really the same thing as 5/5 plus 1/5, or you could say that's the same thing as one and 1/5. 6/5 is equal to one and 1/5, and so what you could do is, you could write the 1/5 part in the fractions column, and then the one well now you're going to be regrouping that into our whole numbers, so you put a one right over there. Notice, 2/5 plus 4/5 is one and 1/5, which is the same thing as 6/5. And then you add the whole number part. One plus five plus three is nine. So you get nine and 1/5. But hopefully you realize that these are really the same idea, just different way of writing things